Teacher Guide: Decimal Concepts

@ Learning Objective 5-10 min lesson

Students will: Explore the relationship between decimals and fractions by expressing decimals to the hundredths as fractions and vice versa, locate decimals on number lines, and compare/order decimals.

Why this matters for FAST: Decimal understanding connects to money, measurement, and fraction operations. FAST questions often require converting between decimals and fractions, comparing decimals, and placing them on number lines.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Base-10 blocks (optional)
Place value chart
Number line printout
Coins (dimes, pennies)

! Common Misconceptions to Address

Misconception #1: Longer Decimals Are Larger

Students think 0.15 > 0.9 because 15 > 9. They're treating decimals like whole numbers.

How to Address:

"Line up the decimals! 0.9 = 0.90 (add a zero). Now compare: 90 hundredths vs 15 hundredths. 0.90 > 0.15. Think about money: 90 cents is more than 15 cents!"

Misconception #2: Confused About Tenths vs Hundredths

Students read 0.25 as "twenty-five tenths" instead of "twenty-five hundredths."

How to Address:

"Count the decimal places! One place = tenths, two places = hundredths. 0.25 has TWO decimal places, so it's 25 hundredths (25/100)."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Show a dollar bill and coins. Ask: "If I have 1 dollar and 50 cents, how do we write that?" ($1.50) "What fraction of a dollar is 50 cents?" (50/100 or 1/2) Connect money to decimals.

2

Introduce the Concept (2 min)

SAY THIS:

"Decimals are another way to write fractions! The first place after the decimal point is TENTHS (1/10). The second place is HUNDREDTHS (1/100). Just like money - dimes are tenths of a dollar, pennies are hundredths!"

Ones

0

.

Tenths

2

Hundredths

5

0.25 = 25/100 = 25 hundredths = 25 cents

3

Teach Decimal-Fraction Connection (2 min)

0.1 = 1/10 (one tenth)
0.5 = 5/10 = 1/2 (five tenths = one half)
0.25 = 25/100 = 1/4 (twenty-five hundredths = one quarter)
0.75 = 75/100 = 3/4 (seventy-five hundredths = three quarters)

4

Comparing Decimals (2 min)

Demonstrate comparing 0.3 and 0.25:

Line up decimal points
Add zeros to make same length: 0.30 vs 0.25
Compare: 30 hundredths > 25 hundredths
So 0.3 > 0.25

Money check: 30 cents > 25 cents!

5

Number Line Placement (2-3 min)

Draw a number line from 0 to 1 with 10 equal parts. Each part = 0.1. Show where 0.5 is (middle), then 0.25 (between 0.2 and 0.3), then 0.75 (between 0.7 and 0.8).

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Which is greater: 0.4 or 0.38?"

Correct answer: 0.4 (or 0.40) > 0.38. Think: 40 hundredths > 38 hundredths, or 40 cents > 38 cents.

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Decimal place value Convert decimals to fractions Convert fractions to decimals Compare decimals Put decimals in order Decimals on number lines

^ Differentiation & Extension

For struggling students: Use money heavily! Dimes = tenths, pennies = hundredths. Practice with coins before abstract decimals.

For advanced students: Introduce thousandths. Have them order a mix of fractions and decimals (e.g., order 1/4, 0.3, 0.25, 1/2).

For home: Send Parent Activity sheet. Families can use money and measuring tapes to explore decimals in everyday life.